Former Arsenal youngster Gnabry and arch finisher Robert Lewandowski twice punished Chelsea with deadly one-two combinations to secure a comprehensive win in west London.
Bayern boss Hansi Flick declared Poland hitman Lewandowski to be “in the form of his life” in the build-up to this last-16 first leg, and the 31-year-old duly tapped home a third for the rampant Bavarians.
Chelsea’s miserable night was compounded by a red card for Marcos Alonso, who was dismissed after a Video Assistant Referee review ruled he had whacked Lewandowski in the face.
The Blues will also be without Jorginho for the return leg in Munich on March 18, after the Italy midfielder picked up a cheap yellow card for dissent.
Lewandowski took his season’s tally to a remarkable 43 goals in 39 games for club and country, but in reality, it was the all-court striker’s two assists that sealed Bayern’s victory.
Gnabry never made the grade at Arsenal despite possessing bundles of talent, but he has flourished into a marauding winger of the highest quality at Bayern.
The 24-year-old notched his 16th and 17th goals of an already hugely fruitful club campaign.